document.write( "Question 335414: Mutt and Jeff need to paint a fence. Mutt can do the job alone 4 hours faster than Jeff. If together they work for 18 hours and finish only half of the job, how long would Jeff need to do the job alone? \n" ); document.write( "

Algebra.Com's Answer #240433 by Edwin McCravy(20063) $\"\"$ $\"About$

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Mutt and Jeff need to paint a fence. Mutt can do the job alone 4 hours faster than Jeff. If together they work for 18 hours and finish only half of the job, how long would Jeff need to do the job alone?
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document.write( "Make this chart\r\n" );
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document.write( "                       | Jobs done | Time spent | Rate in jobs/hour\r\n" );
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document.write( "Mutt working alone     |           |            |\r\n" );
document.write( "Jeff working alone     |           |            | \r\n" );
document.write( "Both working together  |           |            |\r\n" );
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document.write( "Let x be the number of hours it takes Jeff to do 1 job, so fill\r\n" );
document.write( "in x for Jeff's time spent, and 1 for the number of jobs:\r\n" );
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document.write( "                       | Jobs done | Time spent | Rate in jobs/hour\r\n" );
document.write( "-------------------------------------------------------------------\r\n" );
document.write( "Mutt working alone     |           |            |\r\n" );
document.write( "Jeff working alone     |     1     |     x      | \r\n" );
document.write( "Both working together  |           |            |\r\n" );
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document.write( "Since Mutt can do the job alone 4 hours faster than Jeff, his time\r\n" );
document.write( "is 4 hours less, so put x-4 for Mutt's time to finish 1 job, and 1\r\n" );
document.write( "for the number of jobs he can finish in that time:\r\n" );
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document.write( "                       | Jobs done | Time spent | Rate in jobs/hour\r\n" );
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document.write( "Mutt working alone     |     1     |    x-4     |\r\n" );
document.write( "Jeff working alone     |     1     |     x      | \r\n" );
document.write( "Both working together  |           |            |\r\n" );
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document.write( "Since if they work together for 18 hours they finish only half of the job,\r\n" );
document.write( "we put 18 for their time working together and 1/2 for the jobs\r\n" );
document.write( "done.\r\n" );
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document.write( "                       | Jobs done | Time spent | Rate in jobs/hour\r\n" );
document.write( "-------------------------------------------------------------------\r\n" );
document.write( "Mutt working alone     |     1     |    x-4     |\r\n" );
document.write( "Jeff working alone     |     1     |     x      | \r\n" );
document.write( "Both working together  |    1/2    |    18      |\r\n" );
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document.write( "Now we fill in the rates by dividing jobs done by time spent:\r\n" );
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document.write( "                       | Jobs done | Time spent | Rate in jobs/hour\r\n" );
document.write( "-------------------------------------------------------------------\r\n" );
document.write( "Mutt working alone     |     1     |    x-4     |    1/(x-4)\r\n" );
document.write( "Jeff working alone     |     1     |     x      |     1/x\r\n" );
document.write( "Both working together  |    1/2    |    18      |  (1/2)/18\r\n" );
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document.write( "Multiply both side by 18 to clear the main denominator on the right\r\n" );
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document.write( "Multiply through by \r\n" );
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document.write( " \r\n" );
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document.write( "That has solutions\r\n" );
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document.write( " and \r\n" );
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document.write( "x = 74.05551275 and x = 1.944487245\r\n" );
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document.write( "We ignore the smaller solution since it makes no sense that Jeff\r\n" );
document.write( "could finish the job in less than 2 hours since together it takes them\r\n" );
document.write( "18 hours to complete only half the job.  So we discard that answer and\r\n" );
document.write( "conclude that it takes Jeff 74.05551275 hours to do the job by\r\n" );
document.write( "himself.\r\n" );
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document.write( "Edwin

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